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August 7th, 2012, 08:43 PM  #1 
Newbie Joined: Aug 2012 Posts: 10 Thanks: 0  Plotting Supply & Demand Curve
Hey everyone, I'm new here, would love some help on this problem. *Note: At market equilibrium, we have Demand = Supply Code: The supply and demand functions for a good are given, respectively, by q = 2p + 10 , p(q + 4) = 60, where p is the price. a) Determine the equilibrium price and quantity, b) Sketch the supply and demand functions in the same graph for q?0. (a) q = 2p + 10 (1) p(q + 4) = 60 (2) substitute (1) into (2) p ( (2p +10) + 4) = 60 2p^2 + 14p  60 = 0 p^2 + 7p  30 = 0 (p + 10) (p  3) = 0 p = 10 or 3 But, price and quantity equilibrium can't be a negative, so p = 3. That's part (a) solved. Now I have no idea how to transition to part (b), help would be appreciated, thanks! 
August 7th, 2012, 08:52 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Plotting Supply & Demand Curve
Since this does not involve the calculus, I have moved the topic to the appropriate forum. Here is a plot of the two functions on the same graph: [attachment=0:2jyfbf79]supplydemand.jpg[/attachment:2jyfbf79] 
August 7th, 2012, 08:59 PM  #3 
Newbie Joined: Aug 2012 Posts: 10 Thanks: 0  Re: Plotting Supply & Demand Curve
How do you derive the coordinates in relation to the supply and demand equation? Given that we know the market equilibrium falls on the (3,16) coordinates.

August 7th, 2012, 09:11 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Plotting Supply & Demand Curve
If we let p be the independent variable, then the first equation: is a line given in slopeintercept form. We know it will have the point (0,10) and since the slope is 2, it will also have the point (1,12). Then we just run a line through these two points. If we solve the second equation for q, we find: We see that this is a hyperbolic curve with vertical asymptote and horizontal asymptote . We also know it contains the point (3,16). It also has the pintercept at (15,0). This is enough information to sketch the curve. 
August 7th, 2012, 09:24 PM  #5 
Newbie Joined: Aug 2012 Posts: 10 Thanks: 0  Re: Plotting Supply & Demand Curve
Thanks Mark. But what if I want p to be on the yaxis and q on the xaxis instead? And wouldn't the supply curve be: q = 2p +10 if q = 0, 0 = 2p+10 p = 5 (0 , 5) cutting through (16, 3) instead? 
August 7th, 2012, 09:39 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Plotting Supply & Demand Curve
Yes, you would find the point (5,0) to be on the line if we extend it to the left. If we wish for q to be the independent variable instead, then we solve both equations for p: (1) (2) [attachment=0:5pfdprrb]supplydemand2.jpg[/attachment:5pfdprrb] 
August 7th, 2012, 09:51 PM  #7 
Newbie Joined: Aug 2012 Posts: 10 Thanks: 0  Re: Plotting Supply & Demand Curve
So, if I want to make a particular variable as the independent value, I'll just assume that it equals to 0? *ps: What kind of software are you using to input the equations and graphs on your answers? I noticed that it's not text based when I tried to highlight it. 
August 7th, 2012, 09:56 PM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Plotting Supply & Demand Curve
If you want a particular variable to be independent, then solve for the other variable. I am using the site http://www.wolframalpha.com/ to plot the graph. For the second graph I used the command: y=(x10)/2,y=60/(x+4) for x = 0 to 20 Then, I hit [ALT][PRT SCRN] to save a screenshot to the clipboard, opened MSPaint and copied, cropped and saved the image, then attached it. 
August 7th, 2012, 09:59 PM  #9 
Newbie Joined: Aug 2012 Posts: 10 Thanks: 0  Re: Plotting Supply & Demand Curve
Got it, thank you so much Mark! You've been a great help.

August 7th, 2012, 10:02 PM  #10 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Plotting Supply & Demand Curve
Glad to help, and welcome to the forum! 

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